Boil water in your favorite pasta pot. Add pasta, about 2 tablespoons of salt, and cook according to package directions.
By this time your pasta should be done. Reserve two cups of pasta water, then drain and add pasta to the skillet with tomatoes and kale. Season the pasta with pepper and a drizzle of olive oil, toss with the vegetables. Add 1/2 cup pasta water to your food processor or blender with the rest of the sauce ingredients and blend 2-3 minutes until smooth and creamy, adding more pasta water if necessary.
Add sauce into pasta and toss (add more pasta water if it still seems dry). Tear fresh basil over everything and drizzle with balsamic vinegar.
Make sure you use PLENTY of pasta water in your sauce. It should be a little runny and easy to toss with the pasta, not gloppy.
Adjust salt as needed if you add too much water.
If your pan isn’t big enough to toss everything together, transfer to a large bowl.
This dinner could probably serve 6, but it is so good that people will want seconds. My family of four nearly finished the whole thing.